Question Set 1: Finding Proportions Under Normal Distributions

In this question set, you will use Minitab to construct normal distributions to find the area under the curve beyond a given value Using Minitab, construct a standard normal distribution to find the area greater than z= 1.80.

Question Set 1_A:

Using Minitab, construct a standard normal distribution to find the area greater than z = 1.80.

• In Minitab (http://app.minitab.com), choose Graph > Probability Distribution Plot > View Probability
• Normal distribution, Mean = 0 and Standard deviation = 1
• Click Options > select 'A specified x (axis) value'
• To find the area "greater than" select 'Right Tail'
• For 'X value' enter 1.8 > OK

Note: Always remember to include a screenshot of your Minitab output (using Insert > Image > Upload Image) for this lab question and all other Minitab-related lab questions.

Fun Fact: A "standard normal distribution" is a normal distribution with a mean=0 and standard deviation=1 and is also known as a "z distribution."

Question Set 1_B

For a standard normal distribution, what is the area above z = 1.80?

(Simply type the answer you found above, using 3 decimal places.)

Question Set 1_C:

Using Minitab, construct a normal distribution with a mean of 100 and standard deviation of 10. Then, find the area greater than x = 118.

• In Minitab, choose Graph > Probability Distribution Plot > View Probability
• Normal distribution, Mean = 100 and Standard deviation = 10
• Click Options > select 'A specified x (axis) value'
• To find the area "greater than" select 'Right Tail'
• For 'X value' enter 118 > OK

Note: Remember to include a screenshot of your Minitab output (using Insert > Image > Upload Image).

Question Set 1_D:

For the normal distribution above with a mean of 100 and a standard deviation of 10, what is the area above x = 118?

(Simply type the answer you found above, using 3 decimal places.)

Question Set 1_E:

By-hand, calculate the z-score for Question 1_C to show why your answers to 1_B and 1_D are the same.

Show your work.

Question Set 2: Hypothesis Testing

In this question set, you are going to conduct a hypothesis test using the approach introduced on page 7.4.1 of the online course notes.

Research Question: Is there evidence that the average avocado price in Pennsylvania is different from the national average of $1.35?

Data were collected from a random sample of 30 grocery stores in Pennsylvania. Minitab was used to compute the following descriptive statistics:

Variable	N	Mean	SE Mean
Price	30	$1.49	0.027

"SE Mean" is the standard error of the mean.

Below, we will use the five-step hypothesis testing procedure outlined below to conduct a hypothesis test to determine if there is evidence that the average avocado price is different from the national average of $1.35.

Question Set 2.1

Step 1: Provide the null and alternative hypotheses:

H₀: (Note: The sign for the null hypothesis is always =.)

H_a: (Note: The sign for the alternative hypothesis is <, > or . Refer to the research question to decide.)

(In Step 1, we should also check the assumptions. Because the sample size is at least 30, we can presume the sampling distribution will be approximately normal and use the z distribution to find the p value.)

Question Set 2.2

Step 2: Calculate the z test statistic using this formula:

z = (sample statistic - null parameter) / standard error

Hints: For the sample statistic, see the statistics provided for the sample. For the null parameter, look at your null hypothesis. For the standard error, see the statistics provided for the sample

Question Set 2.3

Step 3: Use Minitab to compute the p-value (using the z distribution):

• In Minitab, choose Graph > Probability Distribution Plot > View Probability
• Normal distribution, Mean = 0 and Standard deviation = 1
• Click Options > select 'A specified x (axis) value'
• Since the sign for Ha is , select 'Equal Tails'
• For 'X value' enter the z test statistic you computed above > OK

Question Set 2.4

Step 4:Decide to reject or fail to reject the null hypothesis. Specifically, use your p-value above to fill in the following blanks:

Because the p-value is _______ (use 3 decimal places), which is _______ (less or greater) than an alpha-level of 0.05, we ______________ (reject or fail to reject) the null hypothesis.

Question Set 2.5

Step 5: State a real-world conclusion. Specifically, use your answer above to fill in the following blanks:

Thus, there __________ (is or is not) evidence that the average avocado price in the population is different from the national average of $1.35.

Question 2.6 Reflection:

How confident are you in your answers?

What was the most challenging part of the lab?